Jeremy Browne, a Liberal Democrat, said there needs to be a national debate about whether the state should step in to protect young women from having the veil “imposed” on them.

Mr Browne said he is “instinctively uneasy” about banning behaviour, but suggested the measure may still be necessary to ensure freedom of choice for girls in Muslim communities.

The Home Office minister is the first senior Liberal Democrat to raise such deep concerns about Islamic dress in public places. A growing number of Conservative MPs also want the Government to consider a ban.

Nick Clegg, the Deputy Prime Minister, has suggested he may support banning the veil in classrooms, but downplayed the chances of wider restrictions.

He said: “My own view, I don’t think we should end up like different countries where we tell people how they go about their business. I do think there is an issue with teachers in the classroom…that might be an area where a full veil might be inappropriate.”

The debate was given momentum last week when David Cameron’s spokesman said the Prime Minister would have no problem with the veil being banned in his children’s schools.

Tory MPs, including a vice-chairman of the party, have now voiced support for Mr Browne.

Mr Browne told The Telegraph: “I think this is a good topic for national debate. People of liberal instincts will have competing notions of how to protect and promote freedom of choice.”

He added: “I am instinctively uneasy about restricting the freedom of individuals to observe the religion of their choice. That would apply to Christian minorities in the Middle East just as much as religious minorities here in Britain.

“But there is genuine debate about whether girls should feel a compulsion to wear a veil when society deems children to be unable to express personal choices about other areas like buying alcohol, smoking or getting married.

“We should be very cautious about imposing religious conformity on a society which has always valued freedom of expression.”

His comments follow a political row last week over a decision by Birmingham Metropolitan College to ban veils.

The college was accused of discriminating against Muslims when it ordered all students, staff and visitors to remove face coverings so individuals are “easily identifiable at all times”. It then backtracked after a petition attracted 8,000 signatures in 48 hours and the policy drew criticism from politicians.

Under the current guidance, schools are entitled to set their own uniform policy.

Mr Cameron has so far declined to revisit the rules on veils in schools, but his position is coming under pressure as MPs from across the political spectrum speak out.

Downing Street has said the Prime Minister would support a ban on full-face veils in his children’s schools, but insisted the final decision should rest with head teachers.

However, back-bench Tory MPs yesterday suggested that the rules should be changed to instruct schools to enforce a ban on face coverings.

Dr Sarah Wollaston, the MP for Totnes, said the veils are “deeply offensive” and are “making women invisible”. She suggested that the niqab should be banned in schools and colleges.

Writing for The Telegraph, she said: “It would be a perverse distortion of freedom if we knowingly allowed the restriction of communication in the very schools and colleges which should be equipping girls with skills for the modern world. We must not abandon our cultural belief that women should fully and equally participate in society.”

Bob Neill, a vice-chairman of the Conservative Party, backed Mr Browne’s call for a national debate about a ban. “I do think we need to have a serious conversation about it,” he said.

He said that schools should be able to ban children who persist in covering their faces in lessons.

“Schools should be allowed to say if you want to go into lessons in our schools you have got to comply with the rules,” he said. “You can’t allow the teaching of the majority to be undermined, to be disrupted by that.”

Schools and colleges are given the freedom to set their own policies on uniform covering areas such as the length of skirts and suitable haircuts.

Guidance from the Department for Education states that it should be possible for various religious beliefs to be accommodated within individual institutions’ policies.

The right to a particular religious dress code is safeguarded by the Human Rights Act 1998 and must be followed by schools and colleges, it is claimed.

But the guidance says that teachers can lawfully impose policies that “restrict the freedom of pupils to manifest their religion” – for example, by covering their face or carrying the traditional Sikh kirpan dagger – on various grounds.

The DfE guidance, last issued in 2012, says: “Where a school has good reason for restricting an individual’s freedoms, for example, to ensure effective teaching, the promotion of cohesion and good order in the school, the prevention of bullying, or genuine health and safety or security considerations, then the restriction of an individual’s rights to manifest their religion or belief may be justified.”

Peter Bone, the Tory MP for Wellingborough, said: “From a security point of view you need to be able to see the faces of people – in the House of Commons when we go through a division [to vote] we are not allowed to cover our face. There is a security issue here that is worth debating.”

Last week a judge allowed a defendant to enter a plea in a Crown Court case while wearing a full niqab. He is expected to give a ruling on whether she will be allowed to wear the veil throughout her trial, which is due to take place at Blackfriars Crown Court in November.